Greece's Alexis Tsipras has said his left-wing Syriza party has a "clear mandate" after winning a second general election in less than nine months.
But he said Greeks faced a difficult road and recovery from financial crisis would only come through hard work.
Syriza won just over 35%, slightly down on its previous result and still short of an overall majority.
But it will renew its coalition with the nationalist Independent Greeks. Opposition New Democracy gained 28%.
Far-right Golden Dawn came in third with 7%, slightly up on January's poll.
Syriza was first elected in January on an anti-austerity mandate, but was forced to accept tough conditions for Greece's third international bailout.
Sunday's snap election was called after Mr Tsipras lost his majority in August.
Some of his MPs who had opposed the new bailout conditions split to form a new party, but it has failed to get into parliament. Turnout was low.
Analysis: Paul Moss, BBC News, Athens
It has been raining heavily in Athens, a drenching downpour that left one Greek observer looking at the skies, and wryly suggesting that the gods were angry at Sunday's election result.
And it is hard to avoid the suggested symbolism, not of heavenly wrath but of a country where the summer seems to have ended abruptly, and where the celebrations of Syriza supporters last night have now given way to the harsh reality their re-elected government must face.
It has agreed to tough austerity measures insisted on by the IMF and European Union, and now these must be implemented - cuts to pensions, rises in taxes and an end to some of the regulation and financial allowances that have kept many professions protected.
Farmers have already been readying their tractors for road blockades; some of the unemployed are contemplating their own protests. The new government's honeymoon will be a short one.
"I feel vindicated because the Greek people have a clear mandate to carry on fighting inside and outside our country to uphold the pride of our people," Mr Tsipras told supporters in Athens.
"In Europe today, Greece and the Greek people are synonymous with resistance and dignity.
Mr Tsipras was joined at the celebrations by Independent Greeks leader Panos Kammenos.
"Together we will continue the struggle we began seven months ago," Mr Tsipras said.
Among the challenges facing Mr Tsipras will be satisfying international creditors that Greece is meeting the terms of the latest bailout package worth up to €86bn ($97bn, £61bn). It involved more austerity for ordinary Greeks.
Creditors carry out a review in October and there is still some opposition from within Syriza.
The European Commission on Monday urged Syriza to press on with reforms.
"There is a lot of work ahead and no time to lose," spokesman Margaritis Schinas told reporters.
Jeroen Dijsselbloem, who heads the Eurogroup meetings of eurozone finance ministers, said he was "ready to work closely" with the new Greek government.
European Council President Donald Tusk said in a letter to Mr Tsipras that many of the biggest challenges facing the EU were the same as those facing Greece "including the refugee crisis and the creation of sustainable growth and jobs".
The Greek electoral system means the party with the largest number of votes wins a bonus of 50 seats - and Syriza will have 145 seats in the 300-seat parliament, only four fewer than in Mr Tsipras's January victory.
The Independent Greeks party, which is anti-austerity but agrees with Syriza on little else, won 10 seats. New Democracy won 75, Golden Dawn 18.
Mr Tsipras won despite voters' rejection of austerity in a July referendum.
New government's priorities
- In first 100 days: Cut wage and pension costs again, but less than in previous five years (2% increase in workers' pension contributions, 2% increase in pensioners' national insurance contributions)
- Reform early retirement: Decide which categories will qualify for it (and revamp whole pension system before January)
- Recapitalise banks and set timetable for lifting capital controls
- Hold more talks on debt repayments with EU-IMF lenders, with goal of debt relief deal in January
- Adopt more tax reforms: farmers to see income tax double and fuel subsidy scrapped; new penalties for tax evasion (VAT increase was passed in July; corporation tax was raised by 3%, to 29%)
- Privatise more than half of state electricity network (regional airports and much of road network already privatised)
- Liberalise closed professions, eg removing taxi drivers' fixed tariffs
- Reinstate charges in state health service originally scrapped by Syriza (eg €5 charge for visit to doctor)
(Source: Dimitrios Syrrakos, Manchester Metropolitan University)